If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to:

The particular solution of the differential equation $y(\frac{dx}{dy}) = x \log x$ at $x = e$ and $y = 1$ is

The function $f(x)$ satisfies the differential equation $f^2(x) + 4f'(x)f(x) + [f'(x)]^2 = 0$. Find the general solution for $f(x)$,where $c$ is an arbitrary constant.

The equation of the curve passing through $(1, 0)$ and having a slope of $\frac{y - 1}{x^2 + x}$ is:

Find a particular solution satisfying the given condition:
$x(x^{2}-1) \frac{dy}{dx}=1; y=0$ when $x=2$

The solution of the differential equation $e^{-x}(y + 1)dy + (\cos^2 x - \sin 2x)y dx = 0$, given that $y = 1$ when $x = 0$ is